Choose the correct answer below. A. $$ \arcsin \left(-\frac{1}{2}\right)=x $$ B. $$ \arctan \frac{\sqrt{3}}{3}=x $$ C. $$ \arccos \left(-\frac{1}{2}\right)=x $$

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To determine the correct answers for each of the given equations, we need to evaluate each inverse trigonometric function.

A. $$ \arcsin \left(-\frac{1}{2}\right) = x $$

The arcsine function gives the angle whose sine is $$-\frac{1}{2}$$. The sine of $$-\frac{1}{2}$$ corresponds to the angle $$-\frac{\pi}{6}$$ (or $$-30^\circ$$). Since the range of the arcsine function is $$[- \frac{\pi}{2}, \frac{\pi}{2}]$$, we have:
$$
x = -\frac{\pi}{6}
$$

B. $$ \arctan \frac{\sqrt{3}}{3} = x $$

The arctangent function gives the angle whose tangent is $$\frac{\sqrt{3}}{3}$$. The tangent of $$\frac{\pi}{6}$$ (or $$30^\circ$$) is $$\frac{\sqrt{3}}{3}$$. Therefore:
$$
x = \frac{\pi}{6}
$$

C. $$ \arccos \left(-\frac{1}{2}\right) = x $$

The arccosine function gives the angle whose cosine is $$-\frac{1}{2}$$. The cosine of $$\frac{2\pi}{3}$$ (or $$120^\circ$$) is $$-\frac{1}{2}$$. The range of the arccosine function is $$[0, \pi]$$, so:
$$
x = \frac{2\pi}{3}
$$

In summary, the values of $$x$$ for each option are:
- A: $$x = -\frac{\pi}{6}$$
- B: $$x = \frac{\pi}{6}$$
- C: $$x = \frac{2\pi}{3}$$

All three options are correct in terms of their evaluations, but if you are looking for a specific answer or context, please clarify!
A: $$x = -\frac{\pi}{6}$$ B: $$x = \frac{\pi}{6}$$ C: $$x = \frac{2\pi}{3}$$

Choose the correct answer below. A. \( \arcsin \left(-\frac{1}{2}\right)=x \) B. \( \arctan \frac{\sqrt{3}}{3}=x \) C. \( \arccos \left(-\frac{1}{2}\right)=x \)

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